Weighted Hardy and potential operators in the generalized Morrey spaces
The authors study the weighted \(p\rightarrow q\)-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces \(\mathcal L^{p,\varphi }(\mathbb R^n, w)\) defined by an almost increasing function \(\varphi (r)\) and radial type weight \(w(|x|)\) from the Bary-Stechkin-type class. Sufficient conditions are obtained, in terms of some integral inequalities imposed on \(\varphi \) and \(w\), for such a \(p\rightarrow q\)-boundedness. In the case of local spaces the obtained conditions are also necessary. These results are applied to derive a similar weighted \(p\rightarrow q\)-boundedness of the Riesz potential operator.
scientific article; zbMATH DE number 5862730
scientific article